Question

Find the numerical answer to the summation given below.
75
Σ(6η + 10)
n=0

Answer 1

`17860`

Explanation:

To answer this, let's recall a few properties of summations:

`\sum_(i=0)^(n)(a_i+b_i)=\sum_(i=0)^(n)a_i+\sum_(i=0)^(n)b_i\\\\ \sum_(i=0)^(n)(c*a_i)=c*\sum_(i=0)^(n)(a_i)\\\\ \sum_(i=0)^(n)(c)=(n+1)*c`

With these in mind, we can rewrite the given summation as follows:

`\sum_(n=0)^(75)(6n+10)=\sum_(n=0)^(75)6n+\sum_(n=0)^(75)10=6*\sum_(n=0)^(75)n+76*10\\\\ =6*(75*76)/(2) +760=3*75*76+760=17860`